{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T13:14:15Z","timestamp":1725455655560},"publisher-location":"Berlin\/Heidelberg","reference-count":32,"publisher":"Springer-Verlag","isbn-type":[{"type":"print","value":"3540571841"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/bfb0022548","type":"book-chapter","created":{"date-parts":[[2005,11,13]],"date-time":"2005-11-13T06:14:45Z","timestamp":1131862485000},"page":"14-22","source":"Crossref","is-referenced-by-count":3,"title":["Some connections between set theory and computer science"],"prefix":"10.1007","author":[{"given":"Robert","family":"Cowen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"2_CR1","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1002\/malq.19700160306","volume":"16","author":"A. Abian","year":"1970","unstructured":"A. Abian: Generalized completeness theorem and solvability of systems of boolean polynomial equations, Zeitschrift f\u00fcr Mathematische Logik, 16(1970), 263\u2013264.","journal-title":"Zeitschrift f\u00fcr Mathematische Logik"},{"key":"2_CR2","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1112\/jlms\/s2-27.2.193","volume":"27","author":"B. Banaschewski","year":"1983","unstructured":"B. Banaschewski: The power of the ultra-filter theorem, Journal of the London Mathematical Society, ser. 2, 27(1983), 193\u2013202.","journal-title":"Journal of the London Mathematical Society, ser. 2"},{"key":"2_CR3","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1090\/S0002-9939-1973-0319769-3","volume":"41","author":"R. Cowen","year":"1973","unstructured":"R. Cowen: Some combinatorial theorems equivalent to the prime ideal theorem, Proceedings of the American Mathematical Society, 41(1973), 268\u2013273.","journal-title":"Proceedings of the American Mathematical Society"},{"key":"2_CR4","first-page":"23","volume":"14","author":"R. Cowen","year":"1982","unstructured":"R. Cowen: Partition principles for properties of finite character, Reports on Mathematical Logic, 14(1982), 23\u201328.","journal-title":"Reports on Mathematical Logic"},{"key":"2_CR5","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1305\/ndjfl\/1093870310","volume":"24","author":"R. Cowen","year":"1983","unstructured":"R. Cowen: Compactness via prime semilattices, Notre Dame Journal of Formal Logic, 24(1983), 199\u2013204.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2_CR6","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1002\/jgt.3190100207","volume":"10","author":"L. Cowen","year":"1986","unstructured":"L. Cowen, R. Cowen, D. Woodall: Defective colorings of graphs in surfaces: partitions into subgraphs of bounded valency, J. Graph Theory, 10(1986), 187\u2013195.","journal-title":"J. Graph Theory"},{"key":"2_CR7","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1305\/ndjfl\/1093635418","volume":"31","author":"R. Cowen","year":"1990","unstructured":"R. Cowen: Two hypergraph theorems equivalent to BPI, Notre Dame Journal of Formal Logic, 31(1990), 232\u2013239.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2_CR8","first-page":"113","volume":"24","author":"R. Cowen","year":"1991","unstructured":"R. Cowen: Hypergraph Satisfiability, Reports on Mathematical Logic, 24(1991), 113\u2013118.","journal-title":"Reports on Mathematical Logic"},{"key":"2_CR9","unstructured":"R. Cowen: Combinatorial Analytic Tableaux, to appear."},{"key":"2_CR10","doi-asserted-by":"crossref","unstructured":"M. Frick: A survey of (m,k)-colorings. In J. Gimbel, J.W. Kennedy, L.V. Quintas (eds.): Quo Vadis, Graph Theory? (Annals of Discrete Math 55), North Holland, 1993.","DOI":"10.1016\/S0167-5060(08)70374-1"},{"key":"2_CR11","volume-title":"Computers and Intractability","author":"M. Garey","year":"1979","unstructured":"M. Garey, D. Johnson: Computers and Intractability, W. H. Freeman, San Francisco, 1979."},{"key":"2_CR12","doi-asserted-by":"crossref","first-page":"89","DOI":"10.4064\/fm-41-1-89-96","volume":"41","author":"L. Henkin","year":"1954","unstructured":"L. Henkin: Boolean representation through propositional calculus, Fundamenta Mathematica, 41(1954), 89\u201396.","journal-title":"Fundamenta Mathematica"},{"key":"2_CR13","first-page":"31","volume":"121","author":"P. Howard","year":"1983","unstructured":"P. Howard: Binary consistent choice on pairs and a generalization of K\u00f6nig's infinity lemma, Fundamenta Mathematica, 121(1983), 31\u201337.","journal-title":"Fundamenta Mathematica"},{"key":"2_CR14","unstructured":"P. Howard: Weak forms of the Axiom of Choice, unpublished."},{"key":"2_CR15","volume-title":"The Axiom of Choice","author":"T. Jech","year":"1973","unstructured":"T. Jech: The Axiom of Choice, North Holland, Amsterdam, 1973."},{"key":"2_CR16","doi-asserted-by":"crossref","unstructured":"A. Kolany: Satisfiability on hypergraphs, Studia Logica, to appear.","DOI":"10.1007\/BF01057654"},{"key":"2_CR17","first-page":"91","volume":"25","author":"A. Kolany","year":"1991","unstructured":"A. Kolany, P. Wojtylak: Restricted versions of the compactness theorem, Reports on Mathematical Logic, 25(1991), 91\u2013103.","journal-title":"Reports on Mathematical Logic"},{"key":"2_CR18","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1007\/BF02771458","volume":"9","author":"H. L\u00e4uchli","year":"1971","unstructured":"H. L\u00e4uchli: Coloring infinite graphs and the Boolean prime ideal theorem, Israel Journal of Mathematics, 9(1971), 422\u2013429.","journal-title":"Israel Journal of Mathematics"},{"key":"2_CR19","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF01901934","volume":"14","author":"A. Levy","year":"1963","unstructured":"A. Levy: Remarks on a paper by J. Mycielski, Acta Mathematica Academiae Sceintiarum Hungaricae, 14(1963), 125\u2013130.","journal-title":"Acta Mathematica Academiae Sceintiarum Hungaricae"},{"key":"2_CR20","doi-asserted-by":"crossref","first-page":"233","DOI":"10.4064\/fm-38-1-233-237","volume":"38","author":"J. \u0141\u00f3s","year":"1951","unstructured":"J. \u0141\u00f3s, C. Ryll-Nardzewski: On the application of Tychonoff's theorem in mathematical proofs, Fundamenta Mathematica, 38(1951), 233\u2013237.","journal-title":"Fundamenta Mathematica"},{"key":"2_CR21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.4064\/fm-41-1-49-56","volume":"41","author":"J. \u0141\u00f3s","year":"1955","unstructured":"J. \u0141\u00f3s, C. Ryll-Nardzewski: Effectiveness of the representation theory for Boolean algebras, Fundamenta Mathematica, 41(1955), 49\u201356.","journal-title":"Fundamenta Mathematica"},{"key":"2_CR22","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF01901934","volume":"14","author":"J. Mycielski","year":"1963","unstructured":"J. Mycielski: Some remarks and problems on the coloring of infinite graphs and the theorem of Kuratowski, Acta Mathematica Academiae Scientiarum Hungaricae, 14(1963), 125\u2013130. Errata, ibid., 18(1967), 339\u2013340.","journal-title":"Acta Mathematica Academiae Scientiarum Hungaricae"},{"key":"2_CR23","first-page":"439","volume":"12","author":"J. Mycielski","year":"1964","unstructured":"J. Mycielski: Two remarks on Tychonoff's product theorem, Bulletin Academie Polonaise des Sciences, 12(1964), 439\u2013441.","journal-title":"Bulletin Academie Polonaise des Sciences"},{"key":"2_CR24","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1002\/mana.19770790112","volume":"79","author":"Y. Rav","year":"1977","unstructured":"Y. Rav: Variants of Rado's Selection Lemma, and their applications, Mathematische Nachrichten, 79(1977), 145\u2013165.","journal-title":"Mathematische Nachrichten"},{"key":"2_CR25","first-page":"389","volume":"60","author":"H. Rubin","year":"1954","unstructured":"H. Rubin, D. Scott: Some topological theorems equivalent to the Boolean prime ideal theorem, Bulletin of the American Mathematical Society, 60(1954), 389.","journal-title":"Bulletin of the American Mathematical Society"},{"key":"2_CR26","doi-asserted-by":"crossref","unstructured":"T. Schaefer: The complexity of satisfiability problems, Proceedings of the 10th Annual ACM Symposium on the Theory of Computing, 216\u2013226, 1978.","DOI":"10.1145\/800133.804350"},{"key":"2_CR27","doi-asserted-by":"crossref","unstructured":"T. Schaefer: Complexity of decision problems based on finite two-person perfectinformation games, Proceedings of the 8th Annual ACM Symposium on the Theory of Computing, 41\u201349. 1976.","DOI":"10.1145\/800113.803629"},{"key":"2_CR28","doi-asserted-by":"crossref","first-page":"191","DOI":"10.4064\/cm-39-2-191-199","volume":"39","author":"A. Schrijver","year":"1978","unstructured":"A. Schrijver: The dependence of some logical axioms on disjoint transversals and linked systems, Colloquium Mathematicum, 39(1978), 191\u2013199.","journal-title":"Colloquium Mathematicum"},{"key":"2_CR29","first-page":"390","volume":"60","author":"D. Scott","year":"1954","unstructured":"D. Scott: Prime ideal theorems for rings, lattices and Boolean algebras, Bulletin of the American Mathematical Society, 60(1954), p. 390.","journal-title":"Bulletin of the American Mathematical Society"},{"issue":"3","key":"2_CR30","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1145\/1008293.1008294","volume":"5","author":"L. Stockmeyer","year":"1973","unstructured":"L. Stockmeyer: Planar 3-colorability is polynomial complete, SIGACT News 5, 3(July 1973), 19\u201325.","journal-title":"SIGACT News"},{"key":"2_CR31","unstructured":"D. Woodall: Property B and the four-colour problem. In: D.J.A. Welsh, D.R. Woodall(eds.): Combinatorics, IMA, 1972."},{"key":"2_CR32","unstructured":"D. Woodall: Improper colourings of graphs. In: R. Nelson, R.J. Wilson(eds.): Graph Colourings, Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, 1990."}],"container-title":["Lecture Notes in Computer Science","Computational Logic and Proof Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0022548.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,9]],"date-time":"2020-12-09T21:48:54Z","timestamp":1607550534000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0022548"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["3540571841"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/bfb0022548","relation":{},"subject":[]}}