Related papers: There are only two paradoxes

The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…

Since the diagonal lemma plays a key role in the proof of the main limitative theorems of logic, its proof could shed light on the very essence of these fundamental theorems. Yet the lemma is often characterized as one of those important…

Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…

Letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all letters but the copies of $x$ and $y$ we either obtain a word $xyxy\cdots$ (of even or odd length) or a word $yxyx\cdots$ (of even or odd length). A graph $G=(V,E)$ is…

Sandqvis's semantics for classical logic without bivalence resolves the question of an anti-realist account of classical reasoning after Dummett. This paper applies the framework to the essential questions of metamathematics. The system…

The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…

We prove a duality theorem applicable to a a wide range of specialisations, as well as to some generalisations, of tangles in graphs. It generalises the classical tangle duality theorem of Robertson and Seymour, which says that every graph…

We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…

We present a sequent-style proof system for provability logic GL that admits so-called circular proofs. For these proofs, the graph underlying a proof is not a finite tree but is allowed to contain cycles. As an application, we establish…

A 2-dimensional framework is a straight line realisation of a graph in the Euclidean plane. It is radically solvable if the set of vertex coordinates is contained in a radical extension of the field of rationals extended by the squared edge…

We introduce a class of graphs called compound graphs, generalizing rectangles, which are constructed out of copies of a planar bipartite base graph. The main result is that the number of perfect matchings of every compound graph is…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…

Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…

It is proved that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence…

By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs.

According to Chaitin, G\"odel once told him "it doesn't matter which paradox you use [to prove the First Incompleteness Theorem]". In this paper I will present a few infinitary paradoxes and show how to "translate" them to some undecidable…

I humbly introduce a concept I call "Fregean flows," a graph theoretic representation of classical logic, to show how higher-dimensional graph characteristics might be useful to prove or perhaps at best show the provability of simple…

Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…

Given two graphs, a mapping between their edge-sets is cycle-continuous, if the preimage of every cycle is a cycle. The motivation for this notion is Jaeger's conjecture that for every bridgeless graph there is a cycle-continuous mapping to…