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Frege structures for partial applicative theories

R Kahle
1999 Journal of Logic and Computation  
Due to strictness problems, usually the syntactical definition of Frege structures is conceived as a truth theory for total applicative theories.  ...  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.  ...  Frege Structures for partial applicative theories 4.1 Strictness If we want to define Frege structures for partial applicative theories, we get in trouble with possibly undefined terms.  ... 
doi:10.1093/logcom/9.5.683 fatcat:4htbjbkr7zflvp3a4735xkrvzi

Page 4730 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
Three kinds of structures called Frege structures with inductively defined predicates, Frege structures with proof objects, and proof structures are also introduced.  ...  These structures are obtained by generalizing certain aspects of RPT and they are all closely related to Frege structures.”  ... 


2018 The Review of Symbolic Logic  
$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability.  ...  AbstractRecent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either 'Application Constraint' ($AC$) or 'Frege Constraint' ($FC  ...  objects, places in a structure; if they are taken to be univocally specified, they have to be taken to be elements of a particular system exemplifying, possibly partially, the structure of domains of  ... 
doi:10.1017/s1755020318000278 fatcat:jp2gwmkn5femje6rw5s2nk32u4

Page 8377 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
The paper under review is concerned with Frege structures as a truth theory over applicative theories.  ...  Bunder (5-WLG; Wollongong) 03B General logic 2000m:03043 2000m:03042 03B40 03F03 68N18 Kahle, Reinhard (D-TBNG-I; Tiibingen) Frege structures for partial applicative theories. (English summary) J.  ... 

Page 4711 of Mathematical Reviews Vol. , Issue 87i [page]

1987 Mathematical Reviews  
The paper is devoted to theories with a partial predicate for truth (the idea of truth as a partial predicate comes from Kripke).  ...  Salvatore Guccione (Naples) Reinhardt, William N. (1-CO) 87i:03007 Some remarks on extending and interpreting theories with a partial predicate for truth. J. Philos. Logic 15 (1986), no. 2, 219-251.  ... 

Set Theory and Nominalization, Part I

1992 Journal of Logic and Computation  
Frege structures Frege structures are not only solutions to the problem of model existence, but are also systems of set theory in their own right: they single out that part of Frege's theory which  ...  So in a Frege structure, like in any (Fregean) calculus of functions and objects which has variable-binding (and application) through abstraction (resp. application) operators one can take functions into  ...  Set theory and nominalisation, Part I, p.26. Set theory and nominaIisation, Part II, p.22. The total order assumption, p. 10. A system at the cross-roads of functional and logic programming, p.36.  ... 
doi:10.1093/logcom/2.5.579 fatcat:mrzvivrh4jcs3kvsg2f2z2dx5y

Frege's theory of types [article]

Bruno Bentzen
2020 arXiv   pre-print
Frege did not endorse a semantic account of typing, unlike most type theorists who use different types for booleans, natural numbers, products, etc.  ...  Frege never explicitly advocated a doctrine of types like Russell, but a naive type theory can be found in his concept-script in his 1893 Grundgesetze der Arithmetik.  ...  (Grundgesetze §4) Partial saturation creates ambiguity in the interpretation of function application and suggests that Frege actually thinks of binary functions as unary functions from objects to unary  ... 
arXiv:2006.16453v2 fatcat:rw4mmfk7bvc4xf6ht765jkqufa

Page 1486 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
proof theory with applications to computation.  ...  Structures Comput. Sci. 7 (1997), no. 5, 445-452.  ... 

Set Theory and Nominalization, Part II

1992 Journal of Logic and Computation  
Hence we develop a type theory based on Frege structures and use it as a theory of nominalisation.  ...  Frege structures are more conclusive than a solution to domain equations and can be used as models for nominalisation.  ...  Firstly, Turner can prove at least as much in his theory as one can in a theory based on Frege structures.  ... 
doi:10.1093/logcom/2.6.687 fatcat:kpisjoietffs7e5cl2kchc7vqi

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  ...  Frege arithmetic and recovering N from a Frege structure, rather than proceeding in the opposite direction by recovering a Frege structure from N.  ...  ' of number -are recoverable from any model that contains a Frege structure, where the model ·N, s, 0Ò associated with the Frege structure ·E, mÒ is defined (see Bell 1999 Bell , 1555 where PE is the  ... 
doi:10.1111/j.1746-8361.2005.01024.x fatcat:tjgwx72d45ae5muqpntgbxirya

Page 3499 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
The point structures of Part I are strict partial orders (7,<), where T is nonempty.  ...  Frege is unable to elucidate what a function is. The price of accepting his theory is the view that sentences signify truth-values.  ... 

Page 24 of Mathematical Reviews Vol. , Issue 87a [page]

1987 Mathematical Reviews  
A model with signature S, also called an S-structure, is given by specifying carrier sets A, for every s € ©, partial operations for every element of P and relations for every element of R.  ...  The treatment of Peirce’s theory of signs by introducing into the discussion an application of category theory is noteworthy.  ... 

Reform of the construction of the number system with reference to Gottlob Frege

Heinz Griesel
2007 ZDM: Mathematics Education  
Concepts of quantity (ratio-scale) and interval-scale in comparative measurement theory -going beyond Frege -show the way how the negative numbers can be ontologically committed and the operations of addition  ...  Steiner considered Frege's viewpoint of mathematics fundamentals, refined by Tarski's semantics, as suitable for math education.  ...  As already mentioned it would have been more consistent if Frege had demanded not only the application of numbers for measuring but also that the application of multiplication and addition for measuring  ... 
doi:10.1007/s11858-006-0003-2 fatcat:y3m5lshcq5cnvcelepwy5zyvi4

Page 4020 of Mathematical Reviews Vol. 58, Issue 6 [page]

1979 Mathematical Reviews  
He gives criteria for two first-order sentences to represent the same scientific law (be nomologically equivalent) and for one theory to be a reduction of another.  ...  and triadic semantics in Frege.  ... 

The Breadth of the Paradox

Patricia Blanchette
2015 Philosophia Mathematica  
and Entailment" at the Moral Sciences Club, Cambridge University (May 2012) -"Axioms in Frege" at the Grundgesetze conference, New York University (May 2012) -"Axioms and Structure in Frege" at the "The  ...  Analysis in Frege," CUNY Logic Workshop, September 2012 -"(Frege On) Axioms as Foundations" at the "What are Foundations and What are they For?"  ... 
doi:10.1093/philmat/nkv038 fatcat:fvwwxbggsfbm5pnru4duw6pmu4
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