14 papers · 1 filter
An Introduction to Mathematical Logic
Anton Freund
This introduction begins with a section on fundamental notions of mathematical logic, including propositional logic, predicate or first-order logic, completeness, compactness, the…
Normal functions and maximal order types
Anton Freund, Davide Manca
Transformations of well partial orders induce functions on the ordinals, via the notion of maximal order type. In most examples from the literature, these functions are not normal,…
Higman's lemma is stronger for better quasi orders
Anton Freund
We prove that Higman's lemma is strictly stronger for better quasi orders than for well quasi orders, within the framework of reverse mathematics. In fact, we show a stronger resul…
Bachmann-Howard Derivatives
Anton Freund
It is generally accepted that H. Friedman's gap condition is closely related to iterated collapsing functions from ordinal analysis. But what precisely is the connection? We offer…
Patterns of resemblance and Bachmann-Howard fixed points
Anton Freund
Timothy Carlson's patterns of resemblance employ the notion of -elementarity to describe large computable ordinals. It has been conjectured that a relativization of these patt…
Ackermann and Goodstein go functorial
Juan P. Aguilera, Anton Freund, Michael Rathjen +1
We present variants of Goodstein's theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These…