A. Mostowski. A class of models for second order arithmetic. Bulletin de l'Académie Polonaise des Sciences, Série des sciences mathématiques, astronomiques et physiques, vol. 7 (1959), pp. 401–404. - A. Mostowski. Formal system of analysis based on an infinitistic rule of proof. Infinitistic methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 2-9 September 1959, Państwowe Wydawnictwo Naukowe, Warsaw, and Pergamon Press, Oxford, London, New York, and Paris, 1961, pp. 141–166.

1969 ◽  
Vol 34 (1) ◽  
pp. 128-129 ◽  
Author(s):  
H. B. Enderton
Keyword(s):  
New York ◽  
Formal System ◽  
Second Order ◽  
Foundations Of Mathematics ◽  
Second Order Arithmetic ◽  
Order Arithmetic

An infinitistic rule of proof

1968 ◽  
Vol 32 (4) ◽  
pp. 447-451 ◽  
Author(s):  
H. B. Enderton
Keyword(s):  
Formal System ◽  
Peano Arithmetic ◽  
Second Order ◽  
Second Order Arithmetic ◽  
Order Arithmetic

In this paper we consider a fonnal system of second-order Peano arithmetic with a rule of inference stronger than the ω-rule [3]. We also consider the relation to a class of models for analysis (i.e. second-order arithmetic) which lies between the class of ω-models and the class of β-models [5].The notation used is largely that of [3] and [5]. We assume that the reader has some familiarity with at least the ideas of the former. The formal system (A) of Peano arithmetic employed in [3] includes the comprehension axioms and the second-order induction axiom.

scholarly journals Short note: Least fixed points versus least closed points

2021 ◽  
Author(s):  
Gerhard Jäger
Keyword(s):  
Fixed Points ◽  
Short Note ◽  
Second Order ◽  
Second Order Arithmetic ◽  
Order Arithmetic ◽  
Arithmetic Operator

AbstractThis short note is on the question whether the intersection of all fixed points of a positive arithmetic operator and the intersection of all its closed points can proved to be equivalent in a weak fragment of second order arithmetic.

UNDECIDABILITY OF THE THEORIES OF CLASSES OF STRUCTURES

2014 ◽  
Vol 79 (4) ◽  
pp. 1001-1019 ◽  
Author(s):  
ASHER M. KACH ◽  
ANTONIO MONTALBÁN
Keyword(s):  
Direct Product ◽  
Disjoint Union ◽  
Second Order ◽  
Linear Orders ◽  
Second Order Arithmetic ◽  
Order Arithmetic ◽  
Natural Classes ◽  
Product Of Groups

AbstractMany classes of structures have natural functions and relations on them: concatenation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study the (un)decidability of the theory of several natural classes of structures with appropriate functions and relations. For some of these classes of structures, the resulting theory is decidable; for some of these classes of structures, the resulting theory is bi-interpretable with second-order arithmetic.

scholarly journals Periodic points and subsystems of second-order arithmetic

1993 ◽  
Vol 62 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Harvey Friedman ◽  
Stephen G. Simpson ◽  
Xiaokang Yu
Keyword(s):  
Periodic Points ◽  
Second Order ◽  
Second Order Arithmetic ◽  
Order Arithmetic
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