In the mathematical field of set theory, the Solovay model is a model constructed by Robert M. Solovay (1970) in which all of the axioms of Zermelo–Fraenkel...

formalism to prove that sets are measurable. In 1970, Robert M. Solovay constructed the Solovay model, which shows that it is consistent with standard set theory...

Robert Martin Solovay (born December 15, 1938) is an American mathematician working in set theory. Solovay earned his Ph.D. from the University of Chicago...

real numbers are Lebesgue measurable. This is known as the Solovay model. In his proof, Solovay assumed that the existence of inaccessible cardinals is consistent...

because the Solovay model satisfies Z F + D C {\displaystyle {\mathsf {ZF}}+{\mathsf {DC}}} , and every set of real numbers in this model is Lebesgue...

DC, and therefore also ACω, hold in the Solovay model, constructed in 1970 by Robert M. Solovay as a model of set theory without the full axiom of choice...

Zermelo–Fraenkel set theory in the absence of the axiom of choice (see Solovay's model). The Borel measure agrees with the Lebesgue measure on those sets...

fixed complete Boolean algebra. Boolean-valued models were introduced by Dana Scott, Robert M. Solovay, and Petr Vopěnka in the 1960s in order to help...

each of its finite subgraphs requires only two colors. However, in the Solovay model in which every set of real numbers is Lebesgue measurable, G {\displaystyle...

logically equivalent to the axiom of choice.) There exist models such as the Solovay model where all sets of reals are measurable which are consistent...

have the perfect set property, such as Bernstein sets. However, in Solovay's model, which satisfies all axioms of ZF but not the axiom of choice, every...

In quantum information and computation, the Solovay–Kitaev theorem says that if a set of single-qubit quantum gates generates a dense subgroup of SU(2)...

and thus that no infinite parity function exists; this holds in the Solovay model, for instance. Walsh function, a continuous equivalent Parity bit, the...

different types within a multiverse A problem in measure theory–see Solovay model Klee's measure problem, problem of determining how efficiently the measure...

independent of the standard axiomatic system of set theory known as ZFC; Solovay & Tennenbaum (1971) showed that the statement can neither be proven nor...

considered protocol can be considered secure. Although the Baker–Gill–Solovay theorem showed that there exists an oracle A such that PA = NPA, subsequent...

the axiom V=L SOCA Semi open coloring axiom Solovay 1.  Robert M. Solovay 2.  The Solovay model is a model of ZF in which every set of reals is measurable...

the continuum hypothesis, and the construction by Robert M. Solovay of the Solovay model in which all sets of real numbers are Lebesgue measurable. Sierpiński...

imitating Kurt Gödel's constructible hierarchy. Dana Scott and Robert Solovay realized that the use of constructible sets was an unnecessary complication...

Math., vol. 619, Berlin: Springer, pp. 101–117, MR 0485358 Solovay, Robert M. (1970), "A model of set-theory in which every set of reals is Lebesgue measurable"...

inner model, which satisfies ZFC. The sets that are hereditarily definable over a countable sequence of ordinals form an inner model, used in Solovay's theorem...

sharp, establishing that L is the "core model below zero sharp". The work of Solovay isolated another core model L[U], for U an ultrafilter on a measurable...

infinite, it can be replaced with a finite gate set by appealing to the Solovay-Kitaev theorem. Implementation of Boolean functions using the few-qubit...

diamond principle (◊); Martin's axiom (MA); MA + ¬CH (independence shown by Solovay and Tennenbaum). Every Aronszajn tree is special (EATS); We have the following...

almost huge cardinal is also a Vopěnka cardinal. Kanamori, Reinhardt, and Solovay defined seven large cardinal properties between extendibility and hugeness...

published as Silver (1971), where it was denoted by Σ, and rediscovered by Solovay (1967, p.52), who considered it as a subset of the natural numbers and...

supercompact cardinal is a type of large cardinal independently introduced by Solovay and Reinhardt. They display a variety of reflection properties. If λ {\displaystyle...

[1895] "The Rules of Sociological Method" 8th edition, trans. Sarah A. Solovay and John M. Mueller, ed. George E. G. Catlin (1938, 1964 edition), p. 45...

\vdash } p conclude ⊢ {\displaystyle \vdash } □p. The GL model was pioneered by Robert M. Solovay in 1976. Since then, until his death in 1996, the prime...

1090/S0002-9947-01-02926-9. hdl:2445/7783. J. Bagaria & R. Bosch (2004). "Solovay models and forcing extensions". Journal of Symbolic Logic. 69 (3): 742–766...