In his monograph On Numbers and Games, JH Conway introduced a real-closed field
containing the reals and the ordinals as well as a great many less familiar numbers …

We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss,
Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal …

This dissertation has two major threads, one is mathematical, namely descriptive set theory,
the other is philosophical, namely generalisation in mathematics. Descriptive set theory is …

ABSTRACT A probability model is underdetermined when there is no rational reason to
assign a particular infinitesimal value as the probability of single events. Pruss claims that …

In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of JH Conway's
ordered field of surreal numbers was brought to the fore by the first author and employed to …

The class No of surreal numbers, which John Conway discovered while studying
combinatorial games, possesses a rich numerical structure and shares many arithmetic and …

Conway's real closed field No of surreal numbers is a sweeping generalization of the real
numbers and the ordinals to which a number of elementary functions such as log and …

Hyperseries are generalized transseries thatinvolve exponentials, logarithms of a positive
infinitevariable x, as well as so-called transfinite iterators of the exponential and the …

The real line R and Baire space are two of the most fundamental objects in descriptive set
theory and have been studied extensively. In recent years, set theorists have become …

Every Henselian field of residue characteristic 0 admits a truncation-closed embedding in a
field of generalised power series (possibly, with a factor set). As corollaries we obtain the Ax …