Rosser sentences

A remark on equivalent Rosser sentences

An oversight in Guaspari and Solovay’s “Rosser sentences” (1979, Ann. Math. Log., 16, 81) is pointed out and emended. It concerns the premisses of their proof that there are standard proof predicates all of whose Rosser sentences are provably equivalent. The result holds up, but the premisses mentioned in the paper have to be strengthened somewhat.

Arithmetic analogues of McAloon's unique Rosser sentences

Church-Rosser Made Easy

The Church–Rosser theorem states that the λ-calculus is confluent under αand β-reductions. The standard proof of this result is due to Tait and Martin-Löf. In this note, we present an alternative proof based on the notion of acceptable orderings. The technique is easily modified to give confluence of the βη-calculus.

Modular Church-Rosser Modulo

In [12], Toyama proved that the union of two confluent term-rewriting systems that share absolutely no function symbols or constants is likewise confluent, a property called modularity. The proof of this beautiful modularity result, technically based on slicing terms into an homogeneous cap and a so called alien, possibly heterogeneous substitution, was later substantially simplified in [5, 11]...

A Characterization of Weakly Church-Rosser Abstract Reduction Systems That Are Not Church-Rosser

reduction systems (ARS) are abstract structures for studying general properties of rewriting systems. An ARS is just a set equipped with a set of binary relations. Despite this generality many aspects of rewriting systems can be approached in the theory of ARS, such as confluence and normalization. Moreover, important results have been stated and proved in this setting (examples are Newman’s le...