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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). ...##
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Frege structures for partial applicative theories

1999
*
Journal of Logic and Computation
*

Both approaches are compatible with

doi:10.1093/logcom/9.5.683
fatcat:4htbjbkr7zflvp3a4735xkrvzi
*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. ...##
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The Empty Set, The Singleton, and the Ordered Pair

2003
*
Bulletin of Symbolic Logic
*

complexities of Power

doi:10.2178/bsl/1058448674
fatcat:k4hxto6nobgcnfpmr6vbcg3cce
*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*. ...##
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Set Theory and Nominalization, Part I

1992
*
Journal of Logic and Computation
*

Acknowledgments

doi:10.1093/logcom/2.5.579
fatcat:mrzvivrh4jcs3kvsg2f2z2dx5y
*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*. ...##
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Reality is not structured

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*...

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

2005
*
Russell: the Journal of Bertrand Russell Studies
*

Kallen,

doi:10.15173/russell.v25i1.2073
fatcat:dhpons4jkrainp7dezdzd7aczu
*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. ...##
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Our Knowledge of Numbers as Self-Subsistent Objects

2005
*
Dialectica
*

Although

doi:10.1111/j.1746-8361.2005.01024.x
fatcat:tjgwx72d45ae5muqpntgbxirya
*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. ...##
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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). ...##
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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). ...

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

2003
*
Logic and Logical Philosophy
*

How are concrete

doi:10.12775/llp.1995.009
fatcat:w5f5eenporefdcwmeiwo3s42li
*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. ...##
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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. ...##
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Predicative functionals and an interpretation of ⌢ID<ω

1998
*
Annals of Pure and Applied Logic
*

a part of

doi:10.1016/s0168-0072(97)00045-6
fatcat:4wtec5c56zgcdiri3dcihi6qga
*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. ...##
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Russell's Zigzag Path to the Ramified Theory of Types

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. ...

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