Does adding full induction affect the consistency strength of subsystems of second order arithmetic?

"We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran’s deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel’s famous ‘squeezing argument’; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure."

Booked my ticked to Singapore for the AII Graduate Summer School in Logic.

Tallies pretty well with my own thoughts.

math.stackexchange discussion with a great answer by Joel David Hamkins.

Via compactness.

"We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic."

Claims it "remains an open problem".

Discussion of Ed Nelson's claimed results on the inconsistency of PA and PRA on the n-Category Café.

Dan Piponi's port of Fürstenberg's proof to PLT.

Nice Q&A about iterating consistency statements.