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searching for Second-order arithmetic 23 found (101 total)

Takeuti–Feferman–Buchholz ordinal (423 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 (777 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.

Harvey Friedman (mathematician) (687 words) [view diff] no match in snippet view article

Congress of Mathematicians, with a talk titled "Some systems of second order arithmetic and their use", which established the field of reverse mathematics

Positive set theory (573 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 (350 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

Steve Simpson (mathematician) (495 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

Büchi automaton (4,127 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". The Collected Works of J. Richard Büchi. Stanford: Stanford University

Hypercomputation (3,368 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

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

Computable analysis (1,591 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

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

Jordan curve theorem (3,351 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

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

Many-one reduction (1,763 words) [view diff] exact match in snippet view article find links to article

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

Presburger arithmetic (3,248 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

Epsilon number (2,110 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

Automatic sequence (3,157 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 (2,524 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.

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) (4,618 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)