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Page 764 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
mathematics 2004b:03095 03F05 03B40 03D70 03F25 Kahle, Reinhard (P-NUL-C; Lisbon) Universes over Frege structures.  ...  Cantini, Logical frameworks for truth and abstraction, North-Holland, Amsterdam, 1996; MR 97f:03019]. Next, universes over Frege structures are introduced. One defines s €t:=T(ts).  ... 

Frege structures for partial applicative theories

R Kahle
1999 Journal of Logic and Computation  
Both approaches are compatible with the traditional formalizations of Frege structures and preserve the main results, namely abstraction and the proof-theoretic strength.  ...  To investigate Frege structures in a partial framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer.  ...  Introduction Frege structures were introduced by Aczel in [Acz80] as a semantical concept to provide a new concept of sets by means of a partial truth predicate.  ... 
doi:10.1093/logcom/9.5.683 fatcat:4htbjbkr7zflvp3a4735xkrvzi

The Empty Set, The Singleton, and the Ordered Pair

Akihiro Kanamori
2003 Bulletin of Symbolic Logic  
complexities of Power Set, Replacement, and Choice are broached in the formal elaboration of the 'set of'f {} operation.  ...  In the development of modern mathematical logic out of the turbulence of 19th century logic, the emergence of the empty set, the singleton, and the ordered pair as clear and elementary set-theoretic concepts  ...  is no universal set.  ... 
doi:10.2178/bsl/1058448674 fatcat:k4hxto6nobgcnfpmr6vbcg3cce

Set Theory and Nominalization, Part I

1992 Journal of Logic and Computation  
Acknowledgments The author is indebted to the anonymous referees whose suggestions played a crucial role in improving both the form and the contents of the paper.  ...  Moreover, NF has only one universal set, one complement of each set, and one null set. Furthermore, Cantor's theorem does not hold in NF (the universal set is equinumerous to its power set).  ...  In Aczel's Frege structures, the axiom (Vb) is not rejected. In fact the whole of axiom (V) is proven as a theorem in Frege structures and does not need to be asserted as an axiom as with Frege.  ... 
doi:10.1093/logcom/2.5.579 fatcat:mrzvivrh4jcs3kvsg2f2z2dx5y

Reality is not structured

Jeremy Goodman
2016 Analysis  
In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality.  ...  I will argue that reality is not structured in anything like the way that the sentences we use to talk about it are structured.  ...  In particular, they have argued that, if thoughts are structured out of senses in the way Frege imagined them to be, then we should be able to derive a contradiction by an application of Cantorian diagonalization  ... 
doi:10.1093/analys/anw002 fatcat:foscyjooyvb5tkd55nuteczuwu

The Logic of Sinn [review of Kevin C. Klement, Frege and the Logic of Sense and Reference]

Nicholas Griffin
2005 Russell: the Journal of Bertrand Russell Studies  
Kallen, and S. Langer, eds., Structure, Method, and Meaning: Essays in Honor of Henry M.  ...  The paradoxes arise, as Russell realized (and as Frege failed to see) from Cantorean diagonalization arguments based on the realm of Sinne and Gedanken.  ... 
doi:10.15173/russell.v25i1.2073 fatcat:dhpons4jkrainp7dezdzd7aczu

Our Knowledge of Numbers as Self-Subsistent Objects

William Demopoulos
2005 Dialectica  
Although Frege was undoubtedly concerned with both questions, a goal of the present paper is to argue that his success in securing the objectivity of arithmetic depends on a less contentious commitment  ...  The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk-lore observation that the central problem in the philosophy  ...  Frege arithmetic and recovering N from a Frege structure, rather than proceeding in the opposite direction by recovering a Frege structure from N.  ... 
doi:10.1111/j.1746-8361.2005.01024.x fatcat:tjgwx72d45ae5muqpntgbxirya

Page 2679 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
Stahl, Gerold 83g:03001 The diagonal method in set theory and metamathematics. (Spanish) Teorema 11 (1981), no. 1, 27-35.  ...  Sci. 10 (1972), no. 9, 745-763; MR 56 #17364] (pp. 479-507); Matrix structural analysis [in Lecture Notes for the International Research Seminar on the Theory and Application of Finite Element Methods,  ... 

Page 2997 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
Kanovei, Some problems of descriptive set theory and definability in the theory of types (pp. 21-81); V. A. Lyubetskii and E. I. Gordon, Boolean extensions of uniform structures (pp. 82-153); D. P.  ...  Esakia, Diagonal constructions, the Léb formula and rarefied Cantor spaces (pp. 128-143).  ... 

Page 1288 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
96c:03001 03 MATHEMATICAL LOGIC AND FOUNDATIONS 96c:03001 03-01 03-02 03B40 03D20 03D25 03F30 03F40 Smullyan, Raymond M. (1-IN-Q; Bloomington, IN) * Diagonalization and self-reference.  ...  psychologism in German philosophy 1901-1920 (51-83); Richard Tieszen, The philosophy of arithmetic: Frege and Husserl (85- 112); Claire Ortiz Hill, Husserl and Frege on substitutivity (113- 140); J.  ... 

Page 2073 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
The paper at hand treats Poincaré’s interpretation of the diagonal arguments inherent in Richard’s paradox and in Cantor's proof, and argues that Poincaré’s ideas are not at all outdated.  ...  In the latter, there must be an understanding of the structure of the proof and the content of the theorem (perhaps including its relation to other mathematical facts).  ... 

What is a meaningful name? Frege's idea of a radical semanto-ontological analysis

Pirmin Stekeler-Weithofer
2003 Logic and Logical Philosophy  
How are concrete sets and structures constituted in which (parts of) formal, axiomatized, set theory become 'true' statements?  ...  Think, for example, of an expression that 'describes' a diagonal in Cantor's diagonalization procedure.  ... 
doi:10.12775/llp.1995.009 fatcat:w5f5eenporefdcwmeiwo3s42li

Page 2309 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
Summary: “In their correspondence in 1902 and 1903, after dis- cussing the Russell paradox, Russell and Frege discussed the para- dox of propositions considered informally in Appendix B of Rus- sell’s  ...  In addition, the author shows that FL has the interpolation property and that a consistent fluted sentence is universal if and only if the models of y are closed under taking submodels. J. M.  ... 

Predicative functionals and an interpretation of ⌢ID<ω

Jeremy Avigad
1998 Annals of Pure and Applied Logic  
a part of the author's Ph.D. dissertation [5] , and was supported in part by an Alfred E.  ...  Since the strengths of the theories IDn are cofinal in the ordinal Γ0, as a corollary this analysis provides an ordinal-free characterization of the <Γ0-recursive functions. * The work described here comprises  ...  range over the entire power set of the universe of objects, and the logic itself doesn't include any set comprehension axioms.  ... 
doi:10.1016/s0168-0072(97)00045-6 fatcat:4wtec5c56zgcdiri3dcihi6qga

Russell's Zigzag Path to the Ramified Theory of Types

Alasdair Urquhart
1988 Russell: the Journal of Bertrand Russell Studies  
In this paper 1 give a survey of the foundational schemes which Russell considered and rejected in the five years during which his ideas on logic were in a continual state of flux.  ...  THE RAMIFIED THEORY of types was five years in the making. A curious aspect of the historical evolution of the theory is that Russell began and ended with a theory of types.  ...  ACKNOWLEDGMENTS I would like to thank the staff of the Russell Archives and in particular Kenneth Blackwell and Carl Spadoni for their very kind assistance.  ... 
doi:10.15173/russell.v8i1.1735 fatcat:ome4z7rffzd4djqubceaihdkua
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