Speaker
Alberto Marcone
Università Di Udine
Talks at this conference:
Wednesday, 10:00, J222 
WQOs and BQOs in logic I 
The notion of well quasiorder (WQO) is a natural generalization of wellorders to partial orders. Simply put, a partial order is a WQO if it is wellfounded and all its antichains are finite. Several equivalent characterizations of WQO show that the notion is actually quite robust. In the 1960’s NashWilliams introduced a strengthening of WQO he called better quasiorder (BQO). This was instrumental in Laver’s 1971 proof of Fraïssé’s conjecture: the collection of countable linear orders is a WQO under embeddability. In fact all proofs of Fraïssé’s conjecture actually establish Laver’s stronger statement: countable linear orders are a BQO under embeddability. This survey assumes no previous knowledge of WQOs and BQOs: we will start from the definitions and the basic characterizations, then move on to some sample results. We will pay attention to the logic side of the theory, looking at WQO and BQO theory from the viewpoint of ordinal analysis, reverse mathematics and Weihrauch reducibility. For example, it turns out that many proofs and proof techniques in this area require quite strong axioms. 

Wednesday, 11:30, J222 
WQOs and BQOs in logic II 
The notion of well quasiorder (WQO) is a natural generalization of that of wellorder to partial orders. Simply put, a partial order is a WQO if it is wellfounded and all its antichains are finite. Several equivalent characterizations of WQO show that the notion is actually quite robust. In the 1960’s NashWilliams introduced a strengthening of WQO he called better quasiorder (BQO). This was instrumental in Laver’s 1971 proof of Fraïssé’s conjecture: the collection of countable linear orders is a WQO under embeddability. In fact all proofs of Fraïssé’s conjecture actually establish Laver’s stronger statement: countable linear orders are a BQO under embeddability. This survey assumes no previous knowledge of WQOs and BQOs: we will start from the definitions and the basic characterizations, then move on to some sample results. We will pay attention to the logic side of the theory, looking at WQO and BQO theory from the viewpoint of reverse mathematics. In fact many proofs and proof techniques in this area require quite strong axioms. 

Thursday, 10:00, J222 
WQOs and BQOs in logic III 
The notion of well quasiorder (WQO) is a natural generalization of that of wellorder to partial orders. Simply put, a partial order is a WQO if it is wellfounded and all its antichains are finite. Several equivalent characterizations of WQO show that the notion is actually quite robust. In the 1960’s NashWilliams introduced a strengthening of WQO he called better quasiorder (BQO). This was instrumental in Laver’s 1971 proof of Fraïssé’s conjecture: the collection of countable linear orders is a WQO under embeddability. In fact all proofs of Fraïssé’s conjecture actually establish Laver’s stronger statement: countable linear orders are a BQO under embeddability. This survey assumes no previous knowledge of WQOs and BQOs: we will start from the definitions and the basic characterizations, then move on to some sample results. We will pay attention to the logic side of the theory, looking at WQO and BQO theory from the viewpoint of reverse mathematics. In fact many proofs and proof techniques in this area require quite strong axioms. 