An Extension of Gentzen’s Analysis of Logical Deduction to Second-Order Logic

1996 ◽  
pp. 223-226
Author(s):  
O. F. Serebriannikov
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Logical Deduction ◽  
Second Order Logic

Categoricity and the sets

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Set Theory ◽  
Second Order ◽  
Order Logic ◽  
First Order ◽  
The Status ◽  
Second Order Logic ◽  
Philosophy Of Set Theory ◽  
Order Set

In this chapter, the focus shifts from numbers to sets. Again, no first-order set theory can hope to get anywhere near categoricity, but Zermelo famously proved the quasi-categoricity of second-order set theory. As in the previous chapter, we must ask who is entitled to invoke full second-order logic. That question is as subtle as before, and raises the same problem for moderate modelists. However, the quasi-categorical nature of Zermelo's Theorem gives rise to some specific questions concerning the aims of axiomatic set theories. Given the status of Zermelo's Theorem in the philosophy of set theory, we include a stand-alone proof of this theorem. We also prove a similar quasi-categoricity for Scott-Potter set theory, a theory which axiomatises the idea of an arbitrary stage of the iterative hierarchy.

Algorithmic Logic with Stacks and Its Model-Theoretical Properties

1984 ◽  
Vol 7 (4) ◽  
pp. 391-428
Author(s):  
Wiktor Dańko
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Algorithmic Logic ◽  
Second Order Logic

In this paper we propose to transform the Algorithmic Theory of Stacks (cf. Salwicki [30]) into a logic for expressing and proving properties of programs with stacks. We compare this logic to the Weak Second Order Logic (cf. [11, 15]) and prove theorems concerning axiomatizability without quantifiers (an analogon of Łoś-Tarski theorem) and χ 0 - categoricity (an analogon of Ryll-Nardzewski’s theorem).

Monadic second-order logic on finite sequences

2017 ◽  
Vol 52 (1) ◽  
pp. 232-245
Author(s):  
Loris D'Antoni ◽  
Margus Veanes
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Finite Sequences ◽  
Second Order Logic ◽  
Monadic Second Order Logic

An algebraic characterization of indistinguishable cardinals

1970 ◽  
Vol 35 (1) ◽  
pp. 97-104
Author(s):  
A. B. Slomson
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Algebraic Characterization ◽  
Algebraic Criterion ◽  
Characterizable Cardinals ◽  
Second Order Logic ◽  
Interesting Theorem ◽  
Straightforward Proof

Two cardinals are said to beindistinguishableif there is no sentence of second order logic which discriminates between them. This notion, which is defined precisely below, is closely related to that ofcharacterizablecardinals, introduced and studied by Garland in [3]. In this paper we give an algebraic criterion for two cardinals to be indistinguishable. As a consequence we obtain a straightforward proof of an interesting theorem about characterizable cardinals due to Zykov [6].

A Defense of Second-Order Logic

Axiomathes ◽  
2010 ◽  
Vol 20 (2-3) ◽  
pp. 365-383 ◽  
Author(s):  
Otávio Bueno
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Second Order Logic
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