Very weak fragments of weak K\H{o}nig's lemma

TL;DR

This paper explores extremely weak fragments of K\

Contribution

It investigates the computational strength of very weak K\

Findings

Finite a0^{0}_{1}a class has a computable member

Analyzes the reverse mathematics implications of weak Kf6nig's lemma fragments

Provides insights into the logical strength of these weak fragments

Abstract

It is well-known that any finite $\Pi^{0}_{1}$-class of $2^{\mathbb N}$ has a computable member. Then, how can we understand this in the context of reverse mathematics? In this note, we consider several very weak fragments of K\H{o}nig's lemma to answer this qeustion.