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Henkin's completeness proof: forty years later

Hugues Leblanc, Peter Roeper, Michael Thau, George Weaver
1991 Notre Dame Journal of Formal Logic  
Henkin's result has come to be known as the Strong Completeness Theorem for First-Order L.  ...  To commemorate the publication of Henkin's paper, we offer here two new completeness proofs for first-order Z,. 4 The language considered by Henkin had an unspecified number of terms to start with, but  ...  The rule, proposed by Tarski in a lecture of 1927 and published seven years later in Tarski [13] , was called by him-we noted in Section I -the rule of infinite induction.  ... 
doi:10.1305/ndjfl/1093635746 fatcat:6mpiydkek5dtjcov22ushkf4ni

Book Review: Mathematical logic. An introduction to model theory

J. N. Crossley
1979 Bulletin of the American Mathematical Society  
Again a completeness theorem holds paralleling that above for propositional calculus. However, Henkin's proof leads to a different, and more used, formulation.  ...  'Tor a more rigorous [sic] proof of this [the completeness] theorem [for propositional calculus], see Henkin (1949) " (p. 102).  ...  At last there is at hand in this book a systematic and complete (though austere) presentation of the recent extensive developments in category theory leading to the notion of an elementary topos.  ... 
doi:10.1090/s0273-0979-1979-14718-9 fatcat:vbcllp2n3fbgpdz7xpepma5fzi

Page 1201 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
’s completeness proof: forty years later.  ...  set if S is term-complete and maximally consistent.  ... 

Dugundji's Theorem Revisited

Marcelo E. Coniglio, Newton M. Peron
2014 Logica Universalis  
useful Chagrov and Zakharyaschev's criterion of tabularity for modal logics is provided. 4 In [14]. 5 Although it was considered the original Dugundji's article [9], we preferred to follow the clearer proof  ...  This question was resolved by Dugundji eight years later: it was shown that not only Łukasiewicz's matrices, but no finite matrix can be a complete semantics for any system between S1 and S5.  ...  Proof: The proof is similar to the previous one, but now using Proposition 5.2. X = N if X is cofinite N − {0} otherwise .  ... 
doi:10.1007/s11787-014-0106-4 fatcat:6nvr4pa3sbe4vnbqwcdaodtoye

The Proliferation of International Courts and Tribunals: International Adjudication in Ascendance

Roger P. Alford
2000 Proceedings of the ASIL Annual Meeting  
rendered forty-five judgments.  ...  This divestiture is so complete that last year the United States was found to be in noncompliance with its Algiers Accords obligation simply by permitting private parties to file lawsuits in U.S. courts  ... 
doi:10.1017/s027250370005549x fatcat:djunnvt6ybg7tnhimnokywssdm

A brief history of algebraic logic from neat embeddings to rainbow constructions [article]

Tarek Sayed Ahmed
2015 arXiv   pre-print
But then by algebraising the rest of Henkin's proof, we get that rich algebras are representable.  ...  Rich theories occuring in Henkin's completeness proof eliminate existential quantifiers in existential formulas via individual constants more commonly referred to as witnesses.  ...  Proving the strictness of the last inclusion can be easily distilled from the proof of [43, Theorem 36] . The rest of the alleged statements can also be found in [43] .  ... 
arXiv:1508.05840v1 fatcat:xsyr345hgzf4natorz4ds6hy6q

From Hilbert's program to a logic tool box

J. A. Makowsky
2008 Annals of Mathematics and Artificial Intelligence  
At the moment of completion we were in the fourth week of our teaching strike which lasted 10 weeks (October 2007-January 2008), and which was a resounding success.  ...  Act VI: 100 years later -Fixing Frege If only G. Frege had not been so intimidated by B. Russel's letter. C. Wright, P. Geach and H. Hodes suggested, and G.  ...  Our students, however, should rather follow the advise of the Rabbinic Sages, who admonish us not to study Kabbala (Jewish Mysticism) before the mature age of forty years and before serious exposure to  ... 
doi:10.1007/s10472-009-9115-z fatcat:5czgb6guqzb3hdq46spqz24wdy

Book Review: Wittgenstein's lectures on the foundations of mathematics, Cambridge,

G. Kreisel
1978 Bulletin of the American Mathematical Society  
(which is 'useless' if we know that later we shall go much farther); cf. [4]. involved.)  ...  Sure, by the completeness theorem, F A has a proof using only the rules of ordinary predicate calculus, too; but this fact, which is certainly fundamental if the assumptions of t.f. are granted, has turned  ...  scientifically, if not artistically-speaking, such proofs, for example, of the 4-color conjecture, involve incomparably more progress than, say, the use of large cardinals in (ii) above.  ... 
doi:10.1090/s0002-9904-1978-14413-9 fatcat:krecdpjskrab5ps6xinv7cfbd4

On consistency and existence in mathematics [article]

Walter Dean
2020 arXiv   pre-print
The question is related historically to the formulation, proof, and reception of Gödel's Completeness Theorem.  ...  completeness proof.  ...  For instance in the case of Gödel's original proof, b will be a natural number -say 17 -and the case of Henkin's (1949) proof b will be one of countably many witness constants -say c 17 .  ... 
arXiv:2007.10167v1 fatcat:72llgzqmenhivmhgorpdn5xohq

On the finitizability problem in algebraic logic; recent results [article]

Tarek Sayed Ahmed
2013 arXiv   pre-print
The ω extra dimensions play the role of added constants or witnesses in Henkin's classical proof of the completeness theorem.  ...  Furthermore, A can be chosen to be the minimal completion of B. More on that later on, theorems 2.29, 2.32, 4.27) .  ... 
arXiv:1302.1368v1 fatcat:bguykr2afvfajda4qskyr265ge

"Mathematics is the Logic of the Infinite": Zermelo's Project of Infinitary Logic

Jerzy Pogonowski
2021 Studies in Logic, Grammar and Rhetoric  
Set theory had been developing for about forty years as a mathematical theory, and only later did investigations into models of this theory begin. 674 “Mathematics is the Logic of the Infinite”: Zermelo  ...  The algebraic inspiration for Henkin’s work may be traced as follows: 1.  ... 
doi:10.2478/slgr-2021-0042 fatcat:nnowhogl3bhklm234xa7dion7u

The Origin of the Group in Logic and the Methodology of Science

Paolo Mancosu
2018 Journal of Humanistic Mathematics  
Well-known for his new proof of the completeness theorem for first-order logic and the theory of types (1950), and for his work in algebraic logic, Henkin was a principal investigator in all the grants  ...  For this section, see also Henkin's "In Memoriam" [3] . A recent volume celebrating Henkin's work is [15] . The Victor Lenzen Papers are preserved at the Bancroft Library at UC Berkeley.  ... 
doi:10.5642/jhummath.201801.19 fatcat:yklp4r74yrafpocseoca3qluwq

The Literary Impact of Vestiges of Creation

M. Millhauser
1956 Modern Language Quarterly: A Journal of Literary History  
One reason why he did not complete his chosen task, why in this whole direction he did comparatively little after a brilliant start, was that he devoted much of the energy of his last years to works of  ...  See also pages 120 ff. of Leo Henkin’s valuable Darwinism and the English Novel (New York, 1940).  ... 
doi:10.1215/00182702-17-3-213 fatcat:uewefvijwjhzbmwd66d3j5qi44

Page 60 of Mathematical Reviews Vol. 25, Issue Index [page]

Mathematical Reviews  
ness proof: forty years later. 93c:03010 Mo, Shao Kui Establishment of a logical functional calculus.  ...  (English summary) 93m:03017 Hand, Michael Meaning, truth-conditions, and substitutional quantification. 93k:03007 Leblanc, Hugues (with Roeper, Peter; Thau, Michael; Weaver, George) Henkin’s complete-  ... 

The good, the bad and the ugly

Philip Ebert, Stewart Shapiro
2007 Synthese  
In like manner, an analogous abstraction on well-orderings (or relations generally) is inconsistent, falling to the Burali-Forti paradox.  ...  If the theories are first-order, or secondorder with Henkin semantics, then deductive consistency does suffice for satisfiability, in light of Gödel's and Henkin's completeness theorems.  ...  Any attempt to generate a Russell or Burali-Forti paradox on the defined abstracts fails.  ... 
doi:10.1007/s11229-007-9263-9 fatcat:d77yi56kt5ae3jsxfj5z4v27d4
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