V. L. MurskiĬ. Nondiscernible properties of finite systems of identity relations. Soviet mathematics, vol. 12 (1971), pp. 183–186. (English translation by D. M. Pritzker of Néraspozna-vaémyé svojstva konéčnyh sistém toždéstvénnyh sootnošénij, Doklady Akademie Nauk SSSR, vol. 196 (1971), pp. 520–522.) - George F. McNulty. The decision problem for equational bases of algebras. Annals of mathematical logic, vol. 10 (1976), pp. 193–259. - George F. McNulty. Undecidable properties of finite sets of equations. The journal of symbolic logic, vol. 41 (1976), pp. 589–604.

1982 ◽  
Vol 47 (4) ◽  
pp. 903-904
Author(s):  
S. Burris
Keyword(s):  
Mathematical Logic ◽  
English Translation ◽  
Decision Problem ◽  
Nauk Sssr ◽  
Symbolic Logic ◽  
Finite Sets ◽  
Finite Systems

S. K. Thomason. Noncompactness in propositional modal logic. The journal of symbolic logic, vol. 37 no. 4 (for 1972, pub. 1973), pp. 716–720. - Kit Fine. An incomplete logic containing S4. Theoria, vol. 40 (1974), pp. 23–29. - S. K. Thomason. An incompleteness theorem in modal logic. Theoria, vol. 40 (1974), pp. 30–34. - Martin Gerson. The inadequacy of the neighbourhood semantics for modal logic. The journal of symbolic logic, vol. 40 (1975), pp. 141–148. - Martin Sebastian Gerson. An extension of S4 complete for the neighbourhood semantics but incomplete for the relational semantics. Studio logica, vol. 34 (1975), pp. 333–342. - Martin Gerson. A neighbourhood frame for T with no equivalent relational frame. Zeitschrift für mathematische Logik und Grundlugen der Mathematik, vol. 22 (1976), pp. 29–34. - V. B. Šehtman. On incomplete propositional logics. Soviet mathematics, vol. 18 (1977), pp. 985–989. (English translation by B. F. Wells of O népolnyh logikah vyskazyvanij, Doklady Akadémii Nauk SSSR, vol. 235 (1977), pp. 542–545.) - J. F. A. K. van Benthem. Two simple incomplete modal logics. Theoria, vol. 44 (1978), pp. 25–37. - J. F. A. K. van Benthem and W. J. Blok. Transitivity follows from Dummett's axiom. Theoria, vol. 44 (1978), pp. 117–118. - J. F. A. K. van Benthem. Syntactic aspects of modal incompleteness theorems. Theoria, vol. 44 (1978), vol. 45 (1979). pp. 63–77.

1983 ◽  
Vol 48 (2) ◽  
pp. 488-495 ◽  
Author(s):  
R. A. Bull
Keyword(s):  
Modal Logic ◽  
English Translation ◽  
Nauk Sssr ◽  
Symbolic Logic ◽  
Relational Semantics ◽  
Akademii Nauk Sssr ◽  
Doklady Akademii Nauk Sssr ◽  
Propositional Modal Logic ◽  
Relational Frame ◽  
Incompleteness Theorems

Closing the Circle: An Analysis of Emil Post's Early Work

2006 ◽  
Vol 12 (2) ◽  
pp. 267-289 ◽  
Author(s):  
Liesbeth de Mol
Keyword(s):  
Mathematical Logic ◽  
Decision Problem ◽  
Symbolic Logic ◽  
Negative Solution ◽  
Kurt Gödel ◽  
Historical Fact

AbstractIn 1931 Kurt Gödel published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions to mathematical logic and its foundations should not be underestimated. It is the purpose of this article to show that an interest in the early work of Emil Post should be motivated not only by this historical fact, but also by the fact that Post's approach and method differs substantially from those offered by Gödel, Turing and Church. In this paper it will be shown how this method evolved in his early work and how it finally led him to his results.

scholarly journals Relative Necessity and Propositional Quantification

2019 ◽  
Vol 49 (4) ◽  
pp. 703-726
Author(s):  
Alexander Roberts
Keyword(s):  
Mathematical Logic ◽  
Propositional Logic ◽  
Recent Article ◽  
Symbolic Logic ◽  
Philosophical Logic ◽  
Alternative Account ◽  
Standard Account ◽  
Current Article ◽  
Modal Propositional Logic ◽  
Propositional Quantification

AbstractFollowing Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.

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