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, R. M. (1937), "The theory...

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...

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

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

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

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

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

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

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

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

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...

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

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

functions. Such theories include first-order Peano arithmetic and the weaker Robinson arithmetic, and even to a much weaker theory known as R. A common...

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

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

of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said...

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...

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

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

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

{\displaystyle U} . Examples of such arithmetical theories include Robinson arithmetic and stronger theories such as Peano arithmetic. The T k {\displaystyle T_{k}}...

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

Analysis".: 5  Robinson received her PhD degree in 1948 under Alfred Tarski with a dissertation on "Definability and Decision Problems in Arithmetic".: 14  Her...

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...