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Weak arithmetic theories and their models.
 Glivický, Petr ; Mlček, Josef (advisor) ; Pajas, Petr (referee)
In the present thesis we study arithmetical theories in the language of arithmetic L extended by one binary functional symbol for exponentiation. For arbitrary theory in the language of arithmetic it is possible todefine its extension in this new language Le by adding axioms postulatingbasic properties of exponentiation. We consider two axiomatic systems for exponentiation - Exp1 and Exp2. Thus exponentiation is always defined axiomatically in the theories we deal with. We show that in such theories the Fermat's last theorem is unprovable no matter how strong the original theory is. In the thesis we develop a general method of construction of exponential function. This method subsists of "splitting some original exponential function in shorter segments and of rearranging them to form new exponential function which satisfies required properties. As an application of this method three independence results for stronger variants of negation of Fermat's last theorem are prooved. As a first result we construct model of theory Ar + Exp1 defined in the thesis in which the equation x + y = z has nonzero solution for cofinally many 's. The second result allows to expand an arbitrary model of I1 to model of theory Exp2 in which again Fermat's theorem is violated by cofinally many 's. The third result is a construction...
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