Here are some syntax review notes from Haegeman, Chapter 2:
VP
/ \
/ \
V NP
V and NP are in a relationship of sisterhood. They are daughters of the same parent or mother, VP.
A governs B if
(i) A is a governor;
(ii) A and B are sisters.
Governors are heads.
When a V governs an element [its complement or object] and assigns an internal theta role to it, we say that it theta-governs this element. Also: If X is a head and it governs Y then X head-governs Y.
Recall that a verb governs an object, and the head of a phrase governs the complement.
Node A dominates node B if and only if A is higher up in the tree than B and if you can trace a line from A to B going downwards.
A node dominates another with no intervening node between them.
Node A precedes node B if and only if A is to the left of B and neither A dominates B nor B dominates A.
If a node A precedes a node B and there is no intervening node, then A immediately precedes B.
Node A c-commands node B if and only if
(i) A does not dominate B and B does not dominate A; and
(ii) the first branching node dominating A also dominates B.
A governs B if and only if
(i) A is a governor; and
(ii) A c-commands B and B c-commands A.
A c-commands B if and only if A does not dominate B and every X that dominates A also dominates B.
For the choice of X in C-command (2), two options are considered. When X is equated with the first branching node we obtain the c-command definition given in C-command (1). This structural relation is sometimes referred to as strict c-command. Alternatively, X is interpreted as a maximal projection. Under the latter interpretation of (2), A m-commands B.
A governs B if and only if
(i) A is a governor; and
(ii) A m-commands B; and
(iii) no barrier intervenes between A and B.
Maximal projections are barriers to government.
Governors are heads.
The following rules express the general format for phrase structure:
XP --> Spec; X'
X'* --> X'; YP
X' --> X; YP.
The structure of S' can be assimilated to the X'-format as follows:
CP --> Spec; C'
C' --> C; IP
A-positions are potential theta positions, positions to which a theta role can be assigned, i.e. positions such as [Spec, IP] -- that is, the subject position -- and the NP dominated by V'; [NP, V'] -- that is, the verb's complement or object. A-positions are not necessarily assigned a theta role: The subject position may be occupied by an expletive element. Still it counts as an A-position. In traditional terms, we might say that A-positions correspond to positions associated with grammatical functions.
A'-positions are often defined negatively: They are positions that are not A-positions. [Spec, CP] -- that is, the complementizer -- and adjuncts are standardly considered A'-positions.
Recall that English's four complementizers are that, if, whether, for.