__Research article:__

** Samuel R. Buss.
"A note on bootstrapping intuitionistic bounded arithmetic."
In **

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** Abstract: **This paper, firstly, discusses the
relationship between Buss's definition and Cook and Urquhart's definition of BASIC axioms
and of~$IS^1_2$. The two definitions of BASIC axioms are not equivalent; however, each
intuitionistically implies the law of the excluded middle for quantifier-free formulas.
There is an elementary proof that the definitions of~$IS^1_2$ are equivalent which is not
based on realizability or functional interpretations.

Secondly, it is shown that any negated positive consequence of $S^1_2$
is also a theorem of~$IS^1_2$. Some possible additional axioms for~$IS^1_2$ are
investigated.