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https://hdl.handle.net/20.500.12202/1850
Title: | Intuitionistic logic model theory and forcing |
Authors: | Rauch, Harry E. Davis, Martin D. Smullyan, Raymond M. Fitting, Melvin Chris |
Keywords: | Mathematics. |
Issue Date: | 1968 |
Publisher: | ProQuest Dissertations & Theses |
Citation: | Fitting, M. C. (1968, June). Intuitionistic logic model theory and forcing [Publication No. 302391971) [Doctoral dissertation, Yeshiva University]. ==Source: Dissertation Abstracts International, Volume: 29-06, Section: B, page: 2113. |
Abstract: | The independence proofs of Cohen for the axiom of choice, the continuum hypothesis, and the axiom of constructability are re-formulated using s. Kripke's intuitionistic logic model theory·. We define transfinite sequences of intuitionistic.models with a 'class' model limit in a manner exactly analogous to the definition of Godel in the classical case of a transfinite sequence of (domains of) classical models, M∞ , with a 'class' model limit, L. Classical independence results are established by working with the intuitionistic models themselves; no classical models are constructed, no countable classical models are required (though the definition of intuitionistic model is essentially the same as that of forcing.) ¶ An intuitionistic (or forcing) generalization of the R∞: sequence (sets with rank) is defined and some connections between it and Scott and Solovay's boolean valued models for set theory are established. ¶ For completeness sake, the first six chapters provide a complete treatment of s. Krlpke's intuitionistic logic model theory. Completeness proofs are given for tableau and axiomatic systems, compactness and Skolem-Lowenheim theorems ·are established, and relations with classical logic are shown. The connection between Kripke rmodel theory and algebraic model theory is shown in the propositional case. |
Description: | Doctoral dissertation / Open Access |
URI: | https://ezproxy.yu.edu/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:6817161 https://hdl.handle.net/20.500.12202/1850 |
ISBN: | 9798641289694 |
Appears in Collections: | Belfer Graduate School of Science Dissertations 1962 - 1978 |
Files in This Item:
File | Description | Size | Format | |
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Fitting - Intuitionistic Logic Model Theory and Forcing OA.pdf | 55.19 MB | Adobe PDF | View/Open |
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