Related papers: The iterability hierarchy above I3

Magnitude homology is an invariant of enriched categories which generalizes ordinary categorical homology -- the homology of the classifying space of a small category. The classifying space can also be generalized in a different direction:…

We continue the work from [8] and make a small -- but significant -- improvement to the definition of $j$-decomposable system. This provides us with a better lifting of elementary embeddings to symmetric extensions. In particular, this…

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive relation is consistent for every cardinal…

We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions.

We present a pumping lemma for each level of the collapsible pushdown graph hierarchy in analogy to the second author's pumping lemma for higher-order pushdown graphs (without collapse). Using this lemma, we give the first known examples…

In [Bon20], model theoretic characterizations of several established large cardinal notions were given. We continue this work, by establishing such characterizations for Woodin cardinals (and variants), various virtual large cardinals, and…

A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…

This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using…

We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to…

In this paper we prove that the tree property can hold on regular cardinals in an interval which overlaps a strong limit cardinal. This is a crucial milestone in the long term project, tracing back to a question raised by Foreman and…

We introduce the notion of iterated group extensions, which, roughly speaking, is what one obtains by forming a group extension of a group extension. We interpret iterated extensions in terms of group cohomology, in the same way as…

We address the question regarding the structure of the Mitchell order on normal measures. We show that every well founded order can be realized as the Mitchell order on a measurable cardinal $\kappa$ from some large cardinal assumption.

While not obvious from its initial motivation in linear algebra, there are many context where iterated traces can be defined. In this paper we prove a very general theorem about iterated 2-categorical traces. We show that many…

We deal with an iteration theorem of forcing notion with a kind of countable support of nice enough forcing notion which is proper aleph_2-c.c. forcing notions. We then look at some special cases (Q_D 's preceded by random forcing).

We introduce the notion of a hierarchical quandle, which is a generalisation of diquandles and multi-quandles. Using hierarchical quandle colourings, we construct a cocycle invariants for links coloured by quandles.

Let K be a set of infinite cardinals such that the cardinality of K is the first strong limit cardinal greater than uncountably many strong limit cardinals. We construct a family of pairwise non-embeddable groups which contains 2^k groups…

Suppose there is a Reinhardt cardinal. Then (1) $M_n(X)$ exists and is fully iterable (above $X$) for every transitive set $X$ and every $n<\omega$ (here $M_n(X)$ denotes the canonical minimal proper class inner model containing $X$ and…

Let c be the cardinality of the continuum. We give a family of pairwise incomparable clones (on a countable base set) 2^c members, all with the same unary fragment, namely the set of all unary operations. We also give, for each n, a family…

We introduce the notion of weakly extendible cardinals and show that these cardinals are characterized in terms of weak compactness of second order logic. The consistency strength and largeness of weakly extendible cardinals are located…

We continue the work begun in OEIS sequence A332636 which presents recursive sequences that have triangles that appear embedded in them. This paper i) generalizes the main result presented in A332636, ii) provides a complete set of…