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Goodmans theorem (1976) states that intuitionistic finite-type arithmetic plus the axiom of choice plus the axiom of relativized dependent choice is conservative over Heyting arithmetic. The same result applies to the extensional variant. This is due to Beeson (1979). In this paper we modify Goodman realizability (1978) and provide a new proof of the extensional case.
In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring that realizers ought to act extensionally on realizers, giving rise to a
We first show that in the function realizability topos every metric space is separable, and every object with decidable equality is countable. More generally, working with synthetic topology, every $T_0$-space is separable and every discrete space is
In 1945, A. W. Goodman and R. E. Goodman proved the following conjecture by P. ErdH{o}s: Given a family of (round) disks of radii $r_1$, $ldots$, $r_n$ in the plane it is always possible to cover them by a disk of radius $R = sum r_i$, provided they
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with that of a c
We use recent results by Bainbridge-Chen-Gendron-Grushevsky-Moeller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability problem for effective tropical canonical divisors in equicharacteristic