{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T13:13:22Z","timestamp":1778764402139,"version":"3.51.4"},"reference-count":36,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2016,4,4]],"date-time":"2016-04-04T00:00:00Z","timestamp":1459728000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2016,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A semantics for quantified modal logic is presented that is based on Kleene\u2019s notion of realizability. This semantics generalizes Flagg\u2019s 1985 construction of a model of a modal version of Church\u2019s Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church\u2019s Thesis and a variant of a modal set theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra\u2019s generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott\u2019s graph model (for the untyped lambda calculus) which witnesses the failure of the stability of nonidentity.<\/jats:p>","DOI":"10.1017\/s1755020316000095","type":"journal-article","created":{"date-parts":[[2016,4,4]],"date-time":"2016-04-04T10:28:19Z","timestamp":1459765699000},"page":"752-809","source":"Crossref","is-referenced-by-count":5,"title":["REALIZABILITY SEMANTICS FOR QUANTIFIED MODAL LOGIC: GENERALIZING FLAGG\u2019S 1985 CONSTRUCTION"],"prefix":"10.1017","volume":"9","author":[{"given":"BENJAMIN G.","family":"RIN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SEAN","family":"WALSH","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,4,4]]},"reference":[{"key":"S1755020316000095_ref3","volume-title":"Boolean-Valued Models and Independence Proofs in Set Theory","volume":"12","author":"Bell","year":"1985"},{"key":"S1755020316000095_ref25","volume-title":"Theory of Recursive Functions and Effective Computability","author":"Rogers","year":"1987"},{"key":"S1755020316000095_ref33","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139168717"},{"key":"S1755020316000095_ref34","volume-title":"Constructivism in Mathematics. 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