On Guessing Whether A Sequence Has A Certain Property

TL;DR

This paper introduces the concept of guessability for sets of natural sequences, characterizes these sets thoroughly, and develops a nonstandard logic with novel proofs for related known results.

Contribution

It defines guessability for sequence sets, develops a nonstandard logic with ellipsis and variable arity functions, and provides new proofs for existing results.

Findings

Thorough characterization of guessable sets of sequences

Development of a nonstandard logic with ellipsis and variable arity functions

New proofs for related known results

Abstract

A concept of "guessability" is defined for sets of sequences of naturals. Eventually, these sets are thoroughly characterized. To do this, a nonstandard logic is developed, a logic containing symbols for the ellipsis as well as for functions without fixed arity. New proofs are given for some seemingly-unrelated known results.