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searching for Second-order arithmetic 24 found (102 total)

Takeuti–Feferman–Buchholz ordinal (467 words) [view diff] exact match in snippet view article find links to article

C A + B I {\displaystyle \Pi _{1}^{1}-CA+BI} , a subsystem of second-order arithmetic Π 1 1 {\displaystyle \Pi _{1}^{1}} -comprehension + transfinite

Beta-model (703 words) [view diff] exact match in snippet view article find links to article

mathematics of subsystems of second-order arithmetic. In this context, a β-model of a subsystem of second-order arithmetic is a model M where for any Σ11

Computable measure theory (85 words) [view diff] no match in snippet view article find links to article

Computation 207:5, pp. 642–659. Stephen G. Simpson (2009), Subsystems of second order arithmetic, 2nd ed., Perspectives in Logic, Cambridge University Press.

Hilbert's program (1,159 words) [view diff] no match in snippet view article find links to article

the consistency of Peano arithmetic. More powerful subsets of second order arithmetic have been given consistency proofs by Gaisi Takeuti and others

Positive set theory (610 words) [view diff] no match in snippet view article find links to article

elements at all, which boosts the theory from the strength of second order arithmetic to the strength of Morse–Kelley set theory with the proper class

Silver's dichotomy (338 words) [view diff] exact match in snippet view article find links to article

versions, which have been compared in strength with subsystems of second-order arithmetic from reverse mathematics, while Silver's dichotomy itself is provably

Büchi-Elgot-Trakhtenbrot theorem (206 words) [view diff] no match in snippet view article find links to article

theorem Courcelle's theorem Büchi, Julius Richard (1960). "Weak second order arithmetic and finite automata". Zeitschrift für Mathematische Logik und Grundlagen

Specker sequence (697 words) [view diff] exact match in snippet view article find links to article

532–540. doi:10.1002/malq.200410048 S. Simpson (1999), Subsystems of second-order arithmetic, Springer. E. Specker (1949), "Nicht konstruktiv beweisbare Sätze

Hypercomputation (3,334 words) [view diff] exact match in snippet view article find links to article

more complicated models he was able to give an interpretation of second-order arithmetic. These models require an uncomputable input, such as a physical

Computable analysis (1,553 words) [view diff] exact match in snippet view article find links to article

Physics, Springer-Verlag. Stephen G. Simpson (1999), Subsystems of second-order arithmetic. Klaus Weihrauch (2000), Computable analysis, Springer, ISBN 3-540-66817-9

Jordan curve theorem (3,270 words) [view diff] exact match in snippet view article find links to article

"The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic", Archive for Mathematical Logic, 46 (5): 465–480, doi:10.1007/s00153-007-0050-6

Many-one reduction (1,718 words) [view diff] exact match in snippet view article find links to article

Dm{\displaystyle {\mathcal {D}}_{m}} is isomorphic to the theory of second-order arithmetic. There is a characterization of Dm{\displaystyle {\mathcal {D}}_{m}}

Steve Simpson (mathematician) (481 words) [view diff] no match in snippet view article

JSTOR 2274508, MR 0947843. Simpson, Stephen G. (1999), Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Berlin: Springer-Verlag, doi:10

Tierkreis (Stockhausen) (2,837 words) [view diff] no match in snippet view article

5, 8, 13, ... ), arithmetic series (1, 2, 3, 4, 5, ... ), and "second order" arithmetic series, in which the difference between consecutive members increases

Presburger arithmetic (3,153 words) [view diff] no match in snippet view article find links to article

Büchi, J. Richard (1962). "On a Decision Method in Restricted Second Order Arithmetic". In Nagel, Ernest; Suppes, Patrick; Tarski, Alfred (eds.). Logic

Turing degree (3,130 words) [view diff] exact match in snippet view article find links to article

⟩ or ⟨ ≤, ′, = ⟩ is many-one equivalent to the theory of true second-order arithmetic. This indicates that the structure of D {\displaystyle {\mathcal

Epsilon number (2,075 words) [view diff] case mismatch in snippet view article find links to article

arithmetic Large countable ordinal Stephen G. Simpson, Subsystems of Second-order Arithmetic (2009, p.387) J.H. Conway, On Numbers and Games (1976) Academic

Veblen function (2,756 words) [view diff] case mismatch in snippet view article find links to article

maint: date and year (link) Stephen G. Simpson, Subsystems of Second-order Arithmetic (2009, p.387) M. Rathjen, Ordinal notations based on a weakly Mahlo

Büchi automaton (2,901 words) [view diff] no match in snippet view article find links to article

model. Büchi, J.R. (1962). "On a Decision Method in Restricted Second Order Arithmetic". The Collected Works of J. Richard Büchi. Stanford: Stanford University

Automatic sequence (3,148 words) [view diff] case mismatch in snippet view article find links to article

doi:10.1016/0304-3975(79)90011-2. Büchi, J. R. (1990). "Weak Second-Order Arithmetic and Finite Automata". The Collected Works of J. Richard Büchi.

Cobham's theorem (2,522 words) [view diff] case mismatch in snippet view article find links to article

sequence that is ultimately periodic Büchi, J. R. (1990). "Weak Second-Order Arithmetic and Finite Automata". The Collected Works of J. Richard Büchi.

Complementation of Büchi automaton (1,217 words) [view diff] no match in snippet view article find links to article

of A. Büchi, J. R. (1962), "On a decision method in restricted second order arithmetic", Proc. International Congress on Logic, Method, and Philosophy

Church's thesis (constructive mathematics) (2,657 words) [view diff] exact match in snippet view article

function of the previous paragraph. For example, the classical weak second-order arithmetic R C A 0 {\displaystyle {\mathsf {RCA_{0}}}} is consistent with

S2S (mathematics) (4,617 words) [view diff] no match in snippet view article

second order variables, not every S2S formula can be expressed in second order arithmetic through just Π11 transfinite recursion (see reverse mathematics)