This article gives an exposition of the theory of arithmetic motivic measure, as developed by J. Denef and F. Loeser. 1. Preliminary Concepts There is much that is odd about motivic measure if it is judged by measure theory in the sense of twentieth century analysis. It does not fit neatly with the tradition of measure in the style of Hausdorff, Haar, and Lebesgue. It is best to view motivic me...

If a cellular automaton (CA) is started with a single ON cell, how many cells will be ON after n generations? For certain “odd-rule” CAs, including Rule 150, Rule 614, and Fredkin’s Replicator, the answer can be found by using the combination of a new transformation of sequences, the run length transform, and some delicate scissor cuts. Several other CAs are also discussed, although the analysi...

A 58-year-old man was referred for resection of a pedunculated polyp, which had a head measuring 3.5×2.8cm and a stalk 1.5cm in diameter, over the sigmoid colon. We initially applied a detachable loop over the stalk, but no total cyanotic change of the polyp head was observed. We applied a second loop, but it became entrapped in the head of the polyp without tightening (●" Fig.1). We attempted ...

We study uncountable structures similar to the Fraïssé limits. The standard inductive arguments from theory are replaced by forcing, so we obtain highly sensitive universe of set theory. In particular, generic investigate exist only in extensions universe. prove that most interesting cases rigid. Moreover, provide a (consistent) example an uncountable, dense reals with group integers as its aut...