This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications, suitable both for classroom use and for individual study.Expand

If a $\Pi^1_2$ sentence of a certain form is provable using E-HA${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is Provable in the classical system RCA.Expand

We study the logical content of several maximality principles related to the finite intersection principle (FIP) in set theory. Classically, these are all equivalent to the axiom of choice, but in… Expand

A formalization of general topology in second-order arithmetic using countably based MF spaces is given and the proposition that every regular countable based MF space is homeomorphic to a complete separable metric space is equivalent to over ACA0.Expand

It is shown that the converse statement, “every countably based MF space which is regular is homeomorphic to a complete separable metric space,” is equivalent to .Expand

It is shown that RT (2,4) cannot be proved with one typical application in an intuitionistic extension of RCA0 to higher types, but that this does not remain true when the law of the excluded middle is added.Expand

The reverse mathematics and computability of countable graph theory is studied, obtaining results that show the existence of a connected component is either provable in $\mathsf{RCA}_0$ or is equivalent to induction for $\Sigma^0_2$ formulas, depending on the formulation of the bound on the number of components.Expand