mathematics, Robinson arithmetic is a finitely axiomatized fragment of first-order Peano arithmetic (PA), first set out by Raphael M. Robinson in 1950. It...

the hyperbolic plane. Robinson arithmetic "Raphael Robinson, Mathematician, 83". The New York Times. February 9, 1995. Robinson, Raphael M. (1971). "Undecidability...

Non-standard model of arithmetic Paris–Harrington theorem Presburger arithmetic Skolem arithmetic Robinson arithmetic Second-order arithmetic Typographical Number...

undecidable. Robinson arithmetic is known to be essentially undecidable, and thus every consistent theory that includes or interprets Robinson arithmetic is also...

theories include first-order Peano arithmetic P A {\displaystyle {\mathsf {PA}}} , the weaker Robinson arithmetic Q {\displaystyle {\mathsf {Q}}} as well...

properties). First-order Peano arithmetic, PA. The "standard" theory of arithmetic. The axioms are the axioms of Robinson arithmetic above, together with the...

system that can interpret Robinson arithmetic can prove its own consistency only if it is inconsistent. Moreover, Robinson arithmetic can be interpreted in...

Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929....

sufficient collection is the set of theorems of Robinson arithmetic Q. Some systems, such as Peano arithmetic, can directly express statements about natural...

these systems cannot contain the theory of Peano arithmetic nor its weak fragment Robinson arithmetic; nonetheless, they can contain strong theorems. In...

elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary...

rational numbers Q, the Quaternion group Q, Robinson arithmetic, a finitely axiomatized fragment of Peano Arithmetic Q value in statistics, the minimum false...

or sometimes the Robinson axioms. The resulting first-order theory, known as Robinson arithmetic, is essentially Peano arithmetic without induction....

Robinson arithmetic is listed here even though it is a variety, because of its closeness to Peano arithmetic. Peano arithmetic. Robinson arithmetic with...

sentences that recursively axiomatize a consistent theory extending Robinson arithmetic. Matiyasevich, Yuri V. (1970). Диофантовость перечислимых множеств...

Skolem arithmetic is weaker than Peano arithmetic, which includes both addition and multiplication operations. Unlike Peano arithmetic, Skolem arithmetic is...

recursive arithmetic Finite-valued logic Heyting arithmetic Peano arithmetic Primitive recursive function Robinson arithmetic Second-order arithmetic Skolem...

T {\displaystyle T} which is consistent, effective and contains Robinson arithmetic ("Q") must be incomplete in this sense, by explicitly constructing...

In mathematical logic, Heyting arithmetic H A {\displaystyle {\mathsf {HA}}} is an axiomatization of arithmetic in accordance with the philosophy of intuitionism...

all classical theories expressing Robinson arithmetic do not have it. Most classical theories, such as Peano arithmetic and ZFC in turn do not validate...

axiomatization does not leave a workable algebraic theory. Indeed, even Robinson arithmetic Q {\displaystyle {\mathsf {Q}}} , which removes induction but adds...

scheme. RCA0 is the fragment of second-order arithmetic whose axioms are the axioms of Robinson arithmetic, induction for Σ0 1 formulas, and comprehension...

side, this leads to theories between the Robinson arithmetic Q {\displaystyle {\mathsf {Q}}} and Peano arithmetic P A {\displaystyle {\mathsf {PA}}} : The...

Solomon Feferman, states that no consistent theory T that contains Robinson arithmetic, Q, can interpret Q plus Con(T), the statement that T is consistent...

proof or not), i.e. strong enough to model a weak fragment of arithmetic (Robinson arithmetic suffices), then the theory cannot prove its own consistency...

H_{\aleph _{0}}} must necessarily contain them as well. Now note that Robinson arithmetic can already be interpreted in ST, the very small sub-theory of Zermelo...

K {\displaystyle \omega _{1}^{\mathrm {CK} }} . Theorem 2.21 Q, Robinson arithmetic (although the definition of the proof-theoretic ordinal for such...

the well-known canonical set theories ZFC and NBG, ST interprets Robinson arithmetic (Q), so that ST inherits the nontrivial metamathematics of Q. For...

output contains all true sentences of arithmetic and no false ones." "Arithmetic" refers to Peano or Robinson arithmetic, but the proof invokes no specifics...

theory, Boolos's axiomatic set theory just adequate for Peano and Robinson arithmetic. List of American philosophers "Can you solve the three gods riddle...